The Fu style, developed by Fu Chen Sung
Choosing a teacher
Internal style principles
Clips of other styles
Scientific research on tai chi
"Better to search for a thousand years than take one step in the wrong direction." Chan buddhist saying.
"In China, there is nothing that is not about politics." Hong Kong folk saying.
Learning tai chi is not like learning how to jog or stretch or do push ups - it is exceedingly subtle and can only be learned from someone who is an expert in actually performing the movements, not just an expert in calling themselves a 'master' or in talking about it.
Most reputable teachers will let you do an introductory class for free so you can see if what they are teaching suits you. Check out more than one school. This will help you form a better idea of who is any good - you could potentially waste a lot of time and effort by joining the nearest class or the first one you stumble across. Avoid any teacher that will not demonstrate the form when you visit (there are actually classes out there were you are expected to pay sight-unseen). Closely watch how they move when doing the form. Judge it by how it conforms to the principles of tai chi. If a teacher's form does not comply with the below basic principles, then they have nothing to teach.
The below links have translations of the "classics" of tai chi, which expand on what I have written above (since the general principles of tai chi are also shared by h'sing yi and bagua, most of the rules apply to them as well).
Kuo Yu-Cheung's principles
Neither Chang Sang Feng of the 13th century nor his area residence (Wu Tang mountain) have anything to do with the development of tai chi. Based on all available evidence (which is quite scant even for recent history) the "tai chi classic" of Chang San Feng was written sometime in the 1800s. This follows the commonplace Chinese practice of attributing works to the famous historical person whose philosophy it most closly resembles. Therefore, be highly suspicious of anyone claiming a linage back to Chang San Feng or Taoists in the Wu Dang mountains.
Chen style is a good style and has been spread by some talented teachers. However, some people jump to the conclusion that being the oldest style it is best. To say that it is best because it is oldest denies the possibility of improvement, and if improvement is not possible then there is no point practicing tai chi or any other kind of internal cultivation. Other people see the foot stomping and flashy movements and think shows it is a superior martial art. This shows they do not understand the principle of concealing the energy internally. Not understanding the basic principles means not qualified to teach.
Yang Lu Chan learnt in Chen village, sometime later moving to Beijing and introduced it to the world. People called it 'long boxing' or 'cotton boxing' because it appeared soft and flowed without breaks. Only around the mid-nineteenth century was it named tai chi, by a poet in the Beijing royal household. When Chen Fa Ke (1887-1957) went to Beijing he was shown a list of Yang Lu Chan's principles of tai chi, and said "If that is tai chi, then Chen style is not tai chi." Yang introduced many innovations and is rightly referred to as "Unbeatable Yang". Chen style contains internal principles and is valuable to learn, and the most suitable style for some people's temperament. However, it should be viewed as an intermediate step in the development from kung fu to tai chi, and it does not contain the important innovations introduced by Yang Lu Chan, and later carried into newer styles.
Tai chi is an internal style. The movement is meant to be internal (inside the body). This is one of the main stregths of internal styles, however it also makes it difficult for a beginner to distinguish the skill level of one performer from another. Modern times have also seen the training practice of push hands turned into a competition, emphasising muscular strength (under highly contrived rules) over actual skill.
Likewise some schools emphasise the martial applications of the movements. To a large extent, tai chi evolved from taizu chang fist (少林 太祖 长拳) kung fu  - schools talking about martial applications all the time devolve the art back to its kung fu origins and lose the essence. One of the earliest principles of tai chi is to "deflect the force of 1000 pounds using only 4 ounces" and this basic idea is not realised if the student is instead occupying themselves with joint locks, grabs, etc. The applications should be only taught sparingly, their purpose is to show how to move the body correctly (and therefore to train an internal martial art), not to train the person in "the superficial techniques of the [external] martial arts." This sort of mistake is often seen when teachers teach both internal and external styles in their school, or teach tai chi as a money making scheme and see this way of teaching as an easy way to bring in more students.
In Chinese styles, the traditional meaning of `master` is someone whose full time job is teaching a style. It is thus a reflection of ability to attract students than a designation reflecting skill levels. Traditionally, a `grandmaster` is someone who develops a complete system. There a few (if any) grandmasters alive in the world today - but do not judged teachers badly for using these titles, they have to compete for business, and often it is just their overzealous students who insist they use them.
The only method of judging a teacher's skill is to learn the principles of tai chi written in the classics, and then to use your own mind to consider whether the form demonstrated by a teacher conforms to the principles - if it does, then they are worth learning from, if not, they are not. It is kafkaesque to value formal qualifications (or medals from competitions) over conformance to the above principles>